Technical glossary

Total: 79 terms across 9 categories. Use Ctrl+F (Cmd+F on macOS) to search a specific term.

Coordinate systems and frames

Equatorial system (RA, Dec)

System based on the celestial equator (projection of the Earth equator). Right ascension (RA) measured along the equator from the vernal equinox, declination (Dec) measured from the equator. Standard in stellar catalogues.

Horizontal system (Az, Alt)

Local system: azimuth (Az) measured from north toward east in the horizon plane, altitude (Alt) measured from the horizon. Depends on the observer.

Ecliptic system (lambda, beta)

Coordinates based on the Earth orbital plane. Useful for the Moon and planets (which orbit near the ecliptic plane).

Galactic system (l, b)

Coordinates aligned with the Milky Way plane. Galactic pole at RA=12h51m, Dec=+27.13°.

ICRS (International Celestial Reference System)

Non-rotating inertial system defined by the IAU in 1997, based on extragalactic quasars from the ICRF. Replaces the J2000 mean equator.

GCRS (Geocentric Celestial Reference System)

Earth-centered version of ICRS. Used for geocentric ephemerides. Includes relativistic effects.

CIRS (Celestial Intermediate Reference System)

IAU 2006 intermediate system, with origin at the CIO (Celestial Intermediate Origin). Replaces the mean equinox.

ITRS (International Terrestrial Reference System)

System fixed to the solid Earth, defined by the geodetic sites of ITRF. Used for geographic coordinates.

WGS84

World Geodetic System 1984. Earth reference ellipsoid: a=6378137 m, f=1/298.257223563. GPS standard.

J2000.0

Standard reference epoch: 1 January 2000, 12h TT (JD 2451545.0). Used as the zero point for precession and nutation.

Ephemerides and theories

Ephemerides

Tables or formulas that give positions of celestial bodies over time. They can be analytical (mathematical series) or numerical (N-body integration).

ELP-2000/82B

Ephemeride Lunaire Parisienne 2000, version 82B. Analytical lunar theory by Chapront-Touze and Chapront (Bureau des Longitudes). 36 series, ~37,000 terms. Precision <1 arcsec in the 1900-2100 window.

VSOP87

Variations Seculaires des Orbites Planetaires, 1987 version. Analytical theory of planetary positions. Variants A (heliocentric Cartesian), D (spherical ecliptic), E (barycentric).

DE440 / DE441

JPL/NASA Development Ephemeris, versions 440 (1550-2650) and 441 (-13000 to +17000). Numerical ephemerides with meter-level precision for the Moon and hundreds of meters for planets.

INPOP

Integration Numerique Planetaire de l Observatoire de Paris. The European equivalent of DE.

EPM

Ephemerides of Planets and Moon, from IAA RAS (Russian). Third high-precision numerical ephemeris.

Astronomical time

UTC (Coordinated Universal Time)

Worldwide civil standard. Defined as TAI minus leap seconds. UTC is adjusted with leap seconds whenever UT1-UTC approaches 0.9s.

UT1

Universal time tied to the actual Earth rotation. UT1-UTC published by IERS, varies between -0.9 and +0.9 seconds.

TAI (International Atomic Time)

Atomic time, no leap seconds. In 2026: TAI - UTC = 37 seconds.

TT (Terrestrial Time)

TT = TAI + 32.184 seconds. Uniform scale, primary for modern ephemerides.

TDB (Barycentric Dynamical Time)

TT corrected for relativistic effects of Earth motion. |TDB - TT| < 1.7 ms over the year.

TCG, TCB

Geocentric and Barycentric coordinated times (IAU 1991). Used in general relativity. Differ from TT/TDB by a linear rate.

ΔT (Delta-T)

TT - UT1. Measures the lag/lead of actual Earth rotation vs atomic time. In 2026: ~75 seconds. Mathematically unpredictable, adjusted from observation.

JD (Julian Date)

Number of days since noon of 1 Jan 4713 BC (proleptic Julian calendar). JD for 2000-01-01 12h TT = 2451545.0.

MJD (Modified Julian Date)

MJD = JD - 2400000.5. Used to avoid large floats. MJD starts at midnight, not noon.

Leap second

Second inserted into UTC to keep |UT1 - UTC| < 0.9s. IERS decision, added on Jun 30 or Dec 31. Can be positive or negative (never negative so far).

Sidereal Time

Time measured by Earth rotation with respect to fixed stars (not the Sun). Sidereal day = 23h 56min 4.0905s.

GMST / GAST

Greenwich Mean / Apparent Sidereal Time. GMST excludes nutation, GAST includes it (= GMST + equation of the equinoxes).

LST (Local Sidereal Time)

Sidereal time at the local meridian. LST = GMST/GAST + geographic longitude (in hours).

Earth motions

Precession

Conical motion of the Earth axis on a ~25,770 year cycle. Caused by Sun-Moon gravitational torque on the equatorial bulge.

Nutation

Small oscillations superimposed on precession, main period 18.6 years. Maximum amplitude ~17 arcsec in longitude.

Δψ (delta psi)

Nutation in longitude. Main component: -17.2 arcsec × sin(Ω) where Ω is the longitude of the lunar node.

Δε (delta epsilon)

Nutation in obliquity. Main component: 9.2 arcsec × cos(Ω).

Polar motion (xp, yp)

Small oscillation of the rotation pole position with respect to the geographic pole. Maximum ~0.3 arcsec. Chandler component (~430 days) + annual.

Annual aberration

Apparent star displacement due to Earth orbital speed (~30 km/s). Maximum ~20.5 arcsec.

Diurnal aberration

Apparent displacement due to Earth rotational speed (~0.46 km/s at the equator). Maximum ~0.32 arcsec.

Light deflection

Light bending by the Sun gravitational field (general relativity). For a body 90° from the Sun: 4 milliarcseconds.

The Moon and its peculiarities

Synodic month

Period between two New Moons: 29.530589 days on average. Basis of the lunar calendar.

Anomalistic month

Period between two consecutive perigees: 27.554550 days on average.

Nodal (draconic) month

Period between consecutive passages through the same node: 27.212221 days.

Sidereal month

Actual lunar orbital period with respect to fixed stars: 27.321661 days.

Perigee / Apogee

Points of minimum/maximum distance between Earth and Moon. Mean perigee ~363,000 km, apogee ~405,000 km.

Supermoon / Micromoon

Full or New Moon close to perigee (≤360,000 km, super) or apogee (≥405,000 km, micro). Popular term, no official IAU definition.

Blue Moon

Modern definition: second Full Moon in a calendar month. Classic definition (Maine Farmers Almanac): third Full Moon in a season with four.

Black Moon

Second New Moon in a calendar month, or absence of a Full Moon in February.

Libration

Apparent Moon oscillations that allow us to see up to 59% of the surface over time. Optical (geometric) + physical (dynamic).

Optical libration in longitude

Due to variable orbital speed (Kepler law) on a constant rotation axis. Amplitude ±7.9°.

Optical libration in latitude

Due to the lunar axis tilt (~6.7°) with respect to the orbital plane. Amplitude ±6.7°.

Physical libration

Small real oscillation of the lunar rotation axis. Amplitude ~0.04° in longitude. Modeled by IAU WGCCRE.

Lunar standstill

Maximum lunar declination on an 18.6-year cycle. Major ~28.7°, minor ~18.3°.

Saros

18-year 11-day 8-hour cycle that repeats eclipses in the same sequence. 223 synodic months.

Selenography

Study of the lunar surface. Selenographic coordinates: longitude (positive eastward), latitude.

Solar colongitude

Selenographic longitude of the terminator. 0° = first quarter, 90° = Full Moon, 180° = last quarter.

Eclipses

Solar eclipse

The Moon blocks the Sun. Total, annular, partial, or hybrid. Happens only at New Moon, with the Moon near a node.

Lunar eclipse

Earth blocks sunlight reaching the Moon. Total, partial, or penumbral. Happens at Full Moon, with the Moon near a node.

Eclipse magnitude

For solar: fraction of the Sun diameter covered by the Moon. For lunar: fraction of the lunar diameter inside the umbra/penumbra.

Gamma (γ)

Minimum distance of the shadow axis to the Earth center, in Earth radii. |γ| < 1 = central eclipse.

Umbra / Penumbra

Umbra = total shadow (total eclipse). Penumbra = partial shadow (partial eclipse).

Besselian elements

Set of polynomials describing the lunar shadow cone for solar eclipse prediction. NASA/USNO standard.

Path of totality

Track of the umbral shadow across the Earth surface during a total solar eclipse. Typical width 100-270 km.

Dynamical time and celestial mechanics

Orbital elements (a, e, i, Ω, ω, M)

Six parameters that define a Keplerian orbit: semi-major axis (a), eccentricity (e), inclination (i), longitude of ascending node (Ω), argument of perigee (ω), mean anomaly (M).

Mean anomaly (M)

M = n × (t - tp), where n = mean motion and tp = perigee epoch. Increases linearly with time.

Eccentric anomaly (E)

Solves the Kepler equation: M = E - e sin(E). Solved iteratively.

True anomaly (ν)

Actual angle of the body from perigee, measured at the focus. Relates to E via tan(ν/2) = sqrt((1+e)/(1-e)) × tan(E/2).

Vis-viva

Orbital speed equation: v² = μ × (2/r - 1/a). For the Moon: v ~ 1.022 km/s at perigee, ~0.964 km/s at apogee.

Delaunay argument

Set (D, ℓ, ℓ′, F) used in ELP-2000: D = Sun-Moon elongation, ℓ = mean anomaly of the Moon, ℓ′ = mean anomaly of the Sun, F = latitude argument.

Refraction and atmosphere

Atmospheric refraction

Bending of light rays by the atmosphere, lifting objects near the horizon. At the horizon: ~35 arcmin.

Bennett 1982

Classical refraction formula, valid 0° to 90°. Takes apparent altitude as input. Standard in marine navigation.

Saemundsson 1986

Inverse of Bennett: takes true altitude as input. More accurate at low altitude.

Horizon dip

For an observer above sea level, the horizon falls below the horizontal plane. Approx 0.0293 × sqrt(altitude_m).

Civil twilight

Sun between 0° and -6° below the horizon. Outdoor reading is still possible.

Nautical twilight

Sun between -6° and -12° below the horizon. Horizon still visible for sextant navigation.

Astronomical twilight

Sun between -12° and -18° below the horizon. Sky not yet fully dark for astronomical observation.

Geodesy and location

Geodetic latitude (φ)

Angle between the ellipsoid normal and the equatorial plane. This is what GPS reports. Differs from geocentric latitude by up to 0.19°.

Geocentric latitude (φ′)

Angle between the Earth-center vector and the equatorial plane. Used in some parallax computations.

Geographic longitude (λ)

Measured from the Greenwich meridian, positive eastward in the modern convention (IAU/IERS), positive westward in some older conventions (pre-2000 USNO).

Altitude (h)

Height above the WGS84 ellipsoid (geometric) or above mean sea level (orthometric). Difference = geoid undulation (up to ~100 m).

Parallax

Apparent position change of an object due to observer motion. Lunar: up to 1°. Solar: ~8.8 arcsec.

Lunar horizontal parallax

Angle subtended by the Earth radius from the Moon. On average: 0.95°. At perigee: 1.01°.

See also: /laboratorio/metodologia, /laboratorio/fontes, /laboratorio/precisao.